Editing Fitness function (section)

=== Weighted sum and penalty functions ===
When optimizing with the weighted sum, the single values of the <math>O</math> objectives are first normalized so that they can be compared. This can be done with the help of costs or by specifying target values and determining the current value as the degree of fulfillment. Costs or degrees of fulfillment can then be compared with each other and, if required, can also be mapped to a uniform fitness scale. [[Without loss of generality]], fitness is assumed to represent a value to be maximized. Each objective <math>o_i</math> is assigned a weight <math>w_i</math> in the form of a percentage value so that the overall raw fitness <math>f_{raw}</math> can be calculated as a weighted sum: <blockquote><math>f_{raw} = \sum_{i=1}^O{o_i \cdot w_i} \quad \mathsf{with} \quad \sum_{i=1}^O{w_i} = 1 </math> </blockquote>A violation of <math>R</math> restrictions <math>r_j</math> can be included in the fitness determined in this way in the form of [[Penalty method|penalty functions]]. For this purpose, a function <math>pf_j(r_j)</math> can be defined for each restriction which returns a value between <math>0</math> and <math>1</math> depending on the degree of violation, with the result being <math>1</math> if there is no violation. The previously determined raw fitness is multiplied by the penalty function(s) and the result is then the final fitness <math>f_{final}</math>:<ref name=":1" /> <blockquote><math>f_{final}= f_{raw} \cdot \prod_{j=1}^R{pf_j(r_j)} = \sum_{i=1}^O{(o_i \cdot w_i)} \cdot \prod_{j=1}^R{pf_j(r_j)}</math> </blockquote>This approach is simple and has the advantage of being able to combine any number of objectives and restrictions. The disadvantage is that different objectives can compensate each other and that the weights have to be defined before the optimization. This means that the compromise lines must be defined before optimization, which is why optimization with the weighted sum is also referred to as the [[Multi-objective optimization#A priori methods|a priori method]].<ref name=":0" /> In addition, certain solutions may not be obtained, see the section on the ''[[Fitness function#Comparison of both types of assessment|comparison of both types of optimization]]''.